Drastic increase in the magnitude of very rare summer-mean vapor pressure deficit extremes

Summers with extremely high vapor pressure deficit contribute to crop losses, ecosystem damages, and wildfires. Here, we identify very rare summer vapor pressure deficit extremes globally in reanalysis data and climate model simulations, and quantify the contributions of temperature and atmospheric moisture anomalies to their intensity. The simulations agree with reanalysis data regarding these physical characteristics of historic vapor pressure deficit extremes, and show a +33/+28% increase in their intensity in the northern/southern mid-latitudes over this century. About half of this drastic increase in the magnitude of extreme vapor pressure deficit anomalies is due to climate warming, since this quantity depends exponentially on temperature. Further contributing factors are increasing temperature variability (e.g., in Europe) and the expansion of soil moisture-limited regions. This study shows that to avoid amplified impacts of future vapor pressure deficit extremes, ecosystems and crops must become more resilient not only to an increasing mean vapor pressure deficit, but additionally also to larger seasonal anomalies of this quantity.

• Supplementary Figures 1-8 Supplementary Method 1 In the following, we detail the derivation of the process attribution to the ∆I of VPD S+ between the historical and end-of-century period.In particular, we focus on refining ∆I T , starting with Eq. 14 and arriving at Eq. 15 shown in the methods (both in the main text): where angle brackets denote the average over all VPD S+ in one hemisphere and in the respective period, which is denoted by the superscript (note that these brackets are omitted in the main text whenever possible without loss of clarity).
For ⟨I T ⟩ hist and ⟨I T ⟩ eoc we proceed as illustrated in the following at the example of ⟨I T ⟩ eoc .We insert the average over all considered VPD S+ of the corresponding term in Eq. 13 (in the main text).Then, we re-write the resulting term as products of means.Hereby it is important to note that ⟨a • b⟩ ̸ = ⟨a⟩ • ⟨b⟩ but rather ⟨a • b⟩ = ⟨a⟩ • ⟨b⟩ + cov(a, b).Hence ⟨I T ⟩ eoc becomes: where the residual summarizes covariance effects.The square brackets denote the average across all land grid cells of one VPD S+ , and angle brackets with superscript eoc then denote averages over the considered VPD S+ in the 2091-2100 period.
Next, we express only ⟨I T ⟩ eoc , expanded according to Supplementary Eq. 2, in terms of the respective historical terms and the respective deltas.That is, all mean values in the end-of-century period are rewritten as the sum of their mean value in the historical period plus a change in the mean value, i.e., ⟨[a]⟩ eoc = ⟨[a]⟩ hist + ∆a.Thus, where the residual again summarizes the effects of covariance (changes).Supplementary Equation 1 now reads: This equation includes all so-called processes that contribute to ∆I, namely the change in I that would result from changing T ′ only (i.e., in absence of a mean warming; T var ), changes in I that would result from a mean warming, i.e., increasing T c , but constant T ′ (T clim ), the effect of changing q-contributions to I (Q), and a residual E. The E summarizes several terms related to covariance and higher orders, which, as we will show a posteriori, are comparably small.

1 .
Additional information regarding the results displayed in Fig.2.a, Variability in intensity (I) and its contributions for summer vapor pressure deficit extremes (VPD S+ ) in ERA5 and CESM2 eval shown as box-plot including median line, a box from the first to the third quartile (IQR), and whiskers extending to the farthest data point lying within 1.5 times the IQR.b, The same as Fig.2b.c-e, Relative contributions to I from temperature anomalies (I T ) (c), from the climatological co-variability between temperature and specific humidity (I qT ) (d), and from dynamically induced humidity anomalies (I qd ) (e).Supplementary Figure2.Correlation between seasonal temperature (T ) and humidity (q) and its change between the hist and eoc period.a-c, The Pearson correlation coefficient r between non-detrended q and T in 1979-2023 in ERA5 (a), and averaged over all CESM2 eval (b) and CESM2 hist subsets (c).Dense and sparse stippling in b indicate regions where the ERA5 value lies below and above the range spanned up by the CESM2 eval subsets, respectively.d, Difference in r averaged over subsets in CESM2 eoc minus that in CESM2 hist .Regions with grey hatching are not considered in this study.

5 .
Difference between CESM2 eoc and CESM2 hist (eoc−hist) of the absolute 40-year return level, i.e., of the sum of the 40-year return level of the vapor pressure deficit anomaly (VPD'; as shown in Supplementary Fig.3) and the climatological mean VPD (VPD c ), compared to differences in VPD c only.a,b, Differences in the absolute 40-year return level (a) and in VPD c (b). c, The percentage by which values shown in a exceed those shown in b.Note that in c, some extremely positive and negatives values occur where changes in VPD c are marginal.